Chelsea conceded late goals in both normal time and extra time to lose 2-1 to Sunderland in the League Cup quarterfinals on Tuesday, while Manchester City also advanced thanks to Edin Dzeko's double at Leicester.
South Korea midfielder Ki Sung-yueng grabbed Sunderland's winner with two minutes left at the Stadium of Light, with Chelsea having been taken to extra time after conceding an 88th-minute equalizer by Fabio Borini.
"Football is about scoring goals and winning matches, not being the best team on the pitch," said Chelsea manager Jose Mourinho, whose largely second-string side wasted a number of chances after Frank Lampard bundled in the opening goal in the 46th.
Like Chelsea, City rested several key players but still had enough to see off second-tier Leicester 3-1, with Dzeko's brace adding to the opener scored by Aleksandar Kolarov from a superb free kick.
Dzeko has been given limited playing time in recent weeks because of the brilliant form of fellow strikers Sergio Aguero and Alvaro Negredo. With Aguero sidelined for at least a month with a calf injury, Dzeko is set to see more action over the busy Christmas period.
In making it to the semifinals for the third time in five years, City took its goal tally for the season to 75 from 25 games.
"It is an important competition," City manager Manuel Pellegrini said. "It is important to win every game you play in and to get to the final at Wembley would be wonderful for the supporters."
The only negative of the evening for City was the sight of right back Pablo Zabaleta hobbling off in the first half, clutching his right hamstring. City's other right back, Micah Richards, is already out injured.